A240168 T(n,k) is the number of unlabeled graphs of n vertices and k edges that have endpoints, where an endpoint is a vertex with degree 1.

0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 5, 4, 2, 1, 1, 2, 4, 8, 13, 15, 16, 11, 5, 2, 1, 1, 2, 4, 9, 19, 35, 55, 75, 83, 72, 51, 29, 13, 5, 2, 1, 1, 2, 4, 10, 22, 50, 105, 196, 338, 511, 649, 695, 627, 473, 304, 172, 83, 35, 14, 5, 2, 1

Offset: 1

Author

Chai Wah Wu, Aug 02 2014

Keywords

• nonn
• tabf

Comments

The length of the rows are 1,1,2,4,7,11,16,22,...: (n-1)*(n-2)/2 + 1 = A152947(n).

T(n,k) = 0 if k > (n-1)*(n-2)/2 + 1. (Cf. A245796)

Examples

			First few rows of irregular triangle are:
..0
..1
..1....1
..1....2....2....1
..1....2....3....5....4....2....1
..1....2....4....8...13...15...16...11....5....2....1
..1....2....4....9...19...35...55...75...83...72...51...29...13....5....2....1
...
		

Crossrefs

Cf. A245796. Sum of n-th row is equal to A141580(n).